The People says Tottenham will offer Bale up to £160,000-a-week to try to keep the Welshman if the club qualifies for the Champions League.
Modric was fined for going on strike and refusing to join Tottenham's US Tour last year in a bid to seal his dream move to the Bernabeu.
The midfielder eventually got his way, joining Real for £33m, but a close friend of 23-year-old Bale said: “Gareth won't be doing a Luka Modric.
“He's not that kind of lad. If there is a decision he has to make, then he'll make it but he's not going to kick up a fuss.
“Of course, Gareth is well aware there is a lot of interest in him but he will leave it down to Tottenham and any other clubs to sort out.
“Tottenham have been very good to Gareth and he won't just forget that. It's impossible to predict what will happen.”